Stochastic Nonlinear Systems in Physics, Chemistry, and Biology : Proceedings of the Workshop Bielefeld, Fed. Rep. Of Germany, October 5–11, 1980

This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch­ astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se­ ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. . Front Matter....Pages I-VIII Front Matter....Pages 1-1 On the Foundations of Kinetic Theory....Pages 2-11 Transition Phenomena in Nonlinear Systems....Pages 12-19 Front Matter....Pages 21-21 Approximation of Discontinuous Processes by Continuous Processes....Pages 22-35 On the Asymptotic Behavior of Motions in Random Flows....Pages 36-41 Front Matter....Pages 43-43 Some Aspects of Fluctuation Theory in Nonequilibrium Systems....Pages 44-52 Aspects of Classical and Quantum Theory of Stochastic Bistable Systems....Pages 53-61 Kinetics of Phase Separation....Pages 62-71 Chemical Instabilities and Broken Symmetry: The Hard Mode Case....Pages 72-83 Front Matter....Pages 85-85 Asymptotic Behavior of Several Dimensional Diffusions....Pages 86-99 Qualitative Theory of Stochastic Non-Linear Systems....Pages 100-113 Front Matter....Pages 115-115 Noise Induced Transitions....Pages 116-126 Noise Induced Transitions in Biological Systems....Pages 127-136 Multiplicative Ornstein Uhlenbeck Noise in Nonequilibrium Phenomena....Pages 137-150 Front Matter....Pages 151-151 Weak Turbulence in Deterministic Systems....Pages 152-153 Stochastic Problems in Population Genetics: Applications of Itô’s Stochastic Integrals....Pages 154-161 Poisson Processes in Biology....Pages 162-171 Front Matter....Pages 173-173 Linear Stochastic Evolution Equation Models for Chemical Reactions....Pages 174-184 Stochastic Measure Processes....Pages 185-199 Front Matter....Pages 201-201 Stochastic Methods in Non-Equilibrium Thermodynamics....Pages 202-212 Fluctuation Dynamics Near Chemical Instabilities....Pages 213-221 Front Matter....Pages 201-201 Transition Phenomena in Nonlinear Optics....Pages 222-230 Front Matter....Pages 231-231 Time-Reversibility in Dynamical Systems....Pages 232-233 Back Matter....Pages 235-240